Lab 2: Fixed figure for assignment 3

lab2/assignment3.R

@@ -98,47 +98,22 @@ test_errors <- c()
 
 cost_function <- function(theta) {
   train_error <- MSE(y_train, as.matrix(X_train) %*% theta)
-  
-  
-  return(train_error)
-}
-
-theta <- rep(0, ncol(X_train))
-
-# res <- optim(
-#   par = theta,
-#   fn = cost_function,
-#   method = "BFGS",
-#   control = list(trace = 1, maxit = 200, REPORT = 1),
-# )
-
-for (i in 1:5000) {
-  
-  print(i)
-  res <- optim(
-    par = theta,
-    fn = cost_function,
-    method = "BFGS",
-    control = list(maxit = 1),
-  )
-  
-  print(res$value)
-  
-  theta <- res$par
-  
   test_error <- MSE(y_test, as.matrix(X_test) %*% theta)
   
   train_errors <<- c(train_errors, res$value)
   test_errors <<- c(test_errors, test_error)
   
-  if (res$convergence == 0) {
-    break
-  }
+  return(train_error)
 }
 
-res$counts
+theta <- rep(0, ncol(X_train))
 
-range <- c(train_errors[501:length(train_errors)], test_errors[501:length(test_errors)])
+res <- optim(
+  par = theta,
+  fn = cost_function,
+  method = "BFGS",
+  control = list(trace = 1, maxit = 200),
+)
 
 plot(
   train_errors,
@@ -147,21 +122,18 @@ plot(
   ylab = "Error",
   xlab = "Iteration",
   main = "Training and Test Errors over Iterations",
-  lty = 1,
-  ylim = c(min(range), max(range)),
-  xlim = c(501, length(train_errors)),
+  ylim = c(0.25, 0.75),
+  xlim = c(501, 10000),
 )
 
-points(test_errors,
-       type = "l",
-       col = "red",
-       lty = 2)
+points(test_errors, type = "l", col = "red", )
 
 legend(
   "topright",
-  legend = c("Training Error", "Test Error"),
-  col = c("blue", "red"),
-  lty = c(1, 2)
+  legend = c("Training Error", "Test Error", "Optimal Test Error"),
+  lty = c(1, 1, 0),
+  col = c("blue", "red", "green"),
+  pch = c(NA, NA, 19),
 )
 
 early_stopping <- which.min(test_errors)
@@ -169,6 +141,11 @@ early_stopping
 
 test_errors[early_stopping]
 
+points(early_stopping,
+       test_errors[early_stopping],
+       col = "green",
+       pch = 19)
+
 optimal_theta <- res$par
 optimal_train_mse <- res$value
 optimal_train_mse